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Combustion


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Combustion
Fourth Edition

Irvin Glassman
Richard A. Yetter

AMSTERDAM • BOSTON • HEIDELBERG • LONDON
NEW YORK • OXFORD • PARIS • SAN DIEGO
SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO


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Academic Press is an imprint of Elsevier
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then “Copyright and Permission” and then “Obtaining Permissions.”
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2

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This Fourth Edition is dedicated to the graduate students, post docs, visiting

academicians, undergraduates, and the research and technical staff who contributed so much to the atmosphere for learning and the technical contributions
that emanated from Princeton’s Combustion Research Laboratory.


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No man can reveal to you aught but that
which already lies half asleep in the dawning
of your knowledge.
If he (the teacher) is wise he does not bid
you to enter the house of his wisdom, but
leads you to the threshold of your own mind.
The astronomer may speak to you of his
understanding of space, but he cannot give
you his understanding.
And he who is versed in the science of
numbers can tell of the regions of weight and
measures, but he cannot conduct you hither.
For the vision of one man lends not its
wings to another man.
Gibran, The Prophet
The reward to the educator lies in his
pride in his students’ accomplishments. The
richness of that reward is the satisfaction in
knowing the frontiers of knowledge have been
extended.

D. F. Othmer


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Contents

Prologue
Preface

CHAPTER 1. CHEMICAL THERMODYNAMICS AND
FLAME TEMPERATURES

xvii
xix

1

A.
B.
C.
D.

Introduction
Heats of reaction and formation
Free energy and the equilibrium constants

Flame temperature calculations
1. Analysis
2. Practical considerations
E. Sub- and super sonic combustion thermodynamics
1. Comparisons
2. Stagnation pressure considerations
Problems

1
1
8
16
16
22
32
32
33
36

CHAPTER 2. CHEMICAL KINETICS

43

A. Introduction
B. Rates of reactions and their temperature dependence
1. The Arrhenius rate expression
2. Transition state and recombination rate theories
C. Simultaneous interdependent reactions
D. Chain reactions
E. Pseudo-first-order reactions and the “fall-off” range

F. The partial equilibrium assumption
G. Pressure effect in fractional conversion
H. Chemical kinetics of large reaction mechanisms
1. Sensitivity analysis
2. Rate of production analysis
3. Coupled thermal and chemical reacting systems
4. Mechanism simplification
Problems

43
43
45
47
52
53
57
60
61
62
63
65
66
68
69


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Contents

CHAPTER 3. EXPLOSIVE AND GENERAL OXIDATIVE
CHARACTERISTICS OF FUELS
A.
B.
C.
D.

75

Introduction
Chain branching reactions and criteria for explosion
Explosion limits and oxidation characteristics of hydrogen
Explosion limits and oxidation characteristics of carbon
monoxide
E. Explosion limits and oxidation characteristics of hydrocarbons
1. Organic nomenclature
2. Explosion limits
3. “Low-temperature” hydrocarbon oxidation mechanisms
F. The oxidation of aldehydes
G. The oxidation of methane
1. Low-temperature mechanism
2. High-temperature mechanism
H. The oxidation of higher-order hydrocarbons
1. Aliphatic hydrocarbons
2. Alcohols
3. Aromatic hydrocarbons
4. Supercritical effects
Problems


75
75
83
91
98
99
103
106
110
112
112
113
117
117
127
129
139
141

CHAPTER 4. FLAME PHENOMENA IN PREMIXED
COMBUSTIBLE GASES

147

A. Introduction
B. Laminar flame structure
C. The laminar flame speed
1. The theory of Mallard and Le Chatelier
2. The theory of Zeldovich, Frank-Kamenetskii, and Semenov

3. Comprehensive theory and laminar flame structure analysis
4. The laminar flame and the energy equation
5. Flame speed measurements
6. Experimental results: physical and chemical effects
D. Stability limits of laminar flames
1. Flammability limits
2. Quenching distance
3. Flame stabilization (low velocity)
4. Stability limits and design
E. Flame propagation through stratified combustible mixtures
F. Turbulent reacting flows and turbulent flames
1. The rate of reaction in a turbulent field
2. Regimes of turbulent reacting flows
3. The turbulent flame speed

147
151
153
156
161
168
176
176
185
191
192
200
201
207
211

213
216
218
231


Contents

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xi

G. Stirred reactor theory
H. Flame stabilization in high-velocity streams
I. Combustion in small volumes
Problems

235
240
250
254

CHAPTER 5. DETONATION

261

A. Introduction
1. Premixed and diffusion flames
2. Explosion, deflagration, and detonation
3. The onset of detonation

B. Detonation phenomena
C. Hugoniot relations and the hydrodynamic theory of
detonations
1. Characterization of the Hugoniot curve and the uniqueness of the
C–J point
2. Determination of the speed of sound in the burned gases for conditions
above the C–J point
3. Calculation of the detonation velocity
D. Comparison of detonation velocity calculations with
experimental results
E. The ZND structure of detonation waves
F. The structure of the cellular detonation front and other
detonation phenomena parameters
1. The cellular detonation front
2. The dynamic detonation parameters
3. Detonation limits
G. Detonations in nongaseous media
Problems

261
261
261
262
264

CHAPTER 6. DIFFUSION FLAMES

311

A. Introduction

B. Gaseous fuel jets
1. Appearance
2. Structure
3. Theoretical considerations
4. The Burke–Schumann development
5. Turbulent fuel jets
C. Burning of condensed phases
1. General mass burning considerations and the evaporation coefficient
2. Single fuel droplets in quiescent atmospheres
D. Burning of droplet clouds
E. Burning in convective atmospheres

311
311
312
316
318
322
329
331
332
337
364
365

265
266
276
282
286

293
297
297
301
302
306
307


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1. The stagnant film case
2. The longitudinally burning surface
3. The flowing droplet case
4. Burning rates of plastics: The small B assumption and radiation effects
Problems

365
367
369
372
374

CHAPTER 7. IGNITION

379


A. Concepts
B. Chain spontaneous ignition
C. Thermal spontaneous ignition
1. Semenov approach of thermal ignition
2. Frank-Kamenetskii theory of thermal ignition
D. Forced ignition
1. Spark ignition and minimum ignition energy
2. Ignition by adiabatic compression and shock waves
E. Other ignition concepts
1. Hypergolicity and pyrophoricity
2. Catalytic ignition
Problems

379
382
384
384
389
395
396
401
402
403
406
407

CHAPTER 8. ENVIRONMENTAL COMBUSTION
CONSIDERATIONS


409

A. Introduction
B. The nature of photochemical smog
1. Primary and secondary pollutants
2. The effect of NOx
3. The effect of SOx
C. Formation and reduction of nitrogen oxides
1. The structure of the nitrogen oxides
2. The effect of flame structure
3. Reaction mechanisms of oxides of nitrogen
4. The reduction of NOx
D. SOx emissions
1. The product composition and structure of sulfur compounds
2. Oxidative mechanisms of sulfur fuels
E. Particulate formation
1. Characteristics of soot
2. Soot formation processes
3. Experimental systems and soot formation
4. Sooting tendencies
5. Detailed structure of sooting flames

409
410
411
411
415
417
418
419

420
436
441
442
444
457
458
459
460
462
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Contents

xiii

6. Chemical mechanisms of soot formation
7. The influence of physical and chemical parameters on soot formation
F. Stratospheric ozone
1. The HOx catalytic cycle
2. The NOx catalytic cycle
3. The ClOx catalytic cycle
Problems

478
482
485

486
487
489
491

CHAPTER 9. COMBUSTION OF NONVOLATILE FUELS

495

A. Carbon char, soot, and metal combustion
B. Metal combustion thermodynamics
1. The criterion for vapor-phase combustion
2. Thermodynamics of metal–oxygen systems
3. Thermodynamics of metal–air systems
4. Combustion synthesis
C. Diffusional kinetics
D. Diffusion-controlled burning rate
1. Burning of metals in nearly pure oxygen
2. Burning of small particles – diffusion versus kinetic limits
3. The burning of boron particles
4. Carbon particle combustion (C. R. Shaddix)
E. Practical carbonaceous fuels (C. R. Shaddix)
1. Devolatilization
2. Char combustion
3. Pulverized coal char oxidation
4. Gasification and oxy-combustion
F. Soot oxidation (C. R. Shaddix)
Problems

495

496
496
496
509
513
520
522
524
527
530
531
534
534
539
540
542
545
548

APPENDIXES

551

APPENDIX A. THERMOCHEMICAL DATA AND
CONVERSION FACTORS

555

Table A1.
Table A2.

Table A3.

Conversion factors and physical constants
Thermochemical data for selected chemical
compounds
Thermochemical data for species included in reaction
list of Appendix C

556
557
646

APPENDIX B. ADIABATIC FLAME TEMPERATURES OF
HYDROCARBONS

653

Table B1.

653

Adiabatic flame temperatures


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Contents


APPENDIX C. SPECIFIC REACTION RATE CONSTANTS

659

Table C1.
Table C2.
Table C3.
Table C4.
Table C5.
Table C6.
Table C7.
Table C8.
Table C9.
Table C10.
Table C11.

659
661
662
663
665
668
673
677
683
684
685

H2/O2 mechanism
CO/H2/O2 mechanism

CH2O/CO/H2/O2 mechanism
CH3OH/CH2O/CO/H2/O2 mechanism
CH4/CH3OH/CH2O/CO/H2/O2 mechanism
C2H6/CH4/CH3OH/CH2O/CO/H2/O2 mechanism
Selected reactions of a C3H8 oxidation mechanism
NxOy/CO/H2/O2 mechanism
HCl/NxOy/CO/H2/O2 mechanism
O3/NxOy/CO/H2/O2 mechanism
SOx/NxOy/CO/H2/O2 mechanism

APPENDIX D. BOND DISSOCIATION ENERGIES OF
HYDROCARBONS

693

Table D1. Bond dissociation energies of alkanes
Table D2. Bond dissociation energies of alkenes, alkynes, and
aromatics
Table D3. Bond dissociation energies of C/H/O compounds
Table D4. Bond dissociation energies of sulfur-containing
compounds
Table D5. Bond dissociation energies of nitrogen-containing
compounds
Table D6. Bond dissociation energies of halocarbons

694

APPENDIX E. FLAMMABILITY LIMITS IN AIR

703


Table E1.

Flammability limits of fuel gases and vapors in air at
25°C and 1 atm

APPENDIX F. LAMINAR FLAME SPEEDS
Table F1.

Table F2.

Table F3.

Burning velocities of various fuels at 25°C air-fuel
temperature (0.31 mol% H2O in air). Burning velocity S
as a function of equivalence ratio φ in cm/s
Burning velocities of various fuels at 100°C air-fuel
temperature (0.31 mol% H2O in air). Burning velocity S
as a function of equivalence ratio φ in cm/s
Burning velocities of various fuels in air as a function
of pressure for an equivalence ratio of 1 in cm/s

695
698
699
700
702

704


713

714

719
720

APPENDIX G. SPONTANEOUS IGNITION TEMPERATURE
DATA

721

Table G1. Spontaneous ignition temperature data

722


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xv

APPENDIX H. MINIMUM SPARK IGNITION ENERGIES AND
QUENCHING DISTANCES

743

Table H1. Minimum spark ignition energy data for fuels in air at
1 atm pressure


744

APPENDIX I. PROGRAMS FOR COMBUSTION KINETICS

747

A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
K.
L.
M.

747
747
748
748
750
752
753
754
754

756
756
756
756

Thermochemical parameters
Kinetic parameters
Transport parameters
Reaction mechanisms
Thermodynamic equilibrium
Temporal kinetics (Static and flow reactors)
Stirred reactors
Shock tubes
Premixed flames
Diffusion flames
Boundary layer flow
Detonations
Model analysis and mechanism reduction

Author Index

759

Subject Index

769


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Prologue

This 4th Edition of “Combustion” was initiated at the request of the publisher,
but it was the willingness of Prof. Richard Yetter to assume the responsibility of co-author that generated the undertaking. Further, the challenge brought
to mind the oversight of an acknowledgment that should have appeared in the
earlier editions.
After teaching the combustion course I developed at Princeton for 25 years,
I received a telephone call in 1975 from Prof. Bill Reynolds, who at the time
was Chairman of the Mechanical Engineering Department at Stanford. Because
Stanford was considering developing combustion research, he invited me to
present my Princeton combustion course during Stanford’s summer semester
that year. He asked me to take in consideration that at the present time their
graduate students had little background in combustion, and, further, he wished
to have the opportunity to teleconference my presentation to Berkeley, Ames,
and Sandia Livermore. It was an interesting challenge and I accepted the invitation as the Standard Oil of California Visiting Professor of Combustion.
My early lectures seemed to receive a very favorable response from those
participating in the course. Their only complaint was that there were no notes
to help follow the material presented. Prof. Reynolds approached me with the
request that a copy of lecture notes be given to all the attendees. He agreed it
was not appropriate when he saw the handwritten copies from which I presented the lectures. He then proposed that I stop all other interactions with my
Stanford colleagues during my stay and devote all my time to writing these
notes in the proper grammatical and structural form. Further, to encourage my
writing he would assign a secretary to me who would devote her time organizing and typing my newly written notes. Of course, the topic of a book became
evident in the discussion. Indeed, eight of the nine chapters of the first edition
were completed during this stay at Stanford and it took another 2 years to finish the last chapter, indexes, problems, etc., of this first edition. Thus I regret
that I never acknowledged with many thanks to Prof. Reynolds while he was

alive for being the spark that began the editions of “Combustion” that have
already been published.
“Combustion, 4th Edition” may appear very similar in format to the 3rd
Edition. There are new sections and additions, and many brief insertions that
are the core of important modifications. It is interesting that the content of
these insertions emanated from an instance that occurred during my Stanford
presentation. At one lecture, an attendee who obviously had some experience
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Prologue

in the combustion field claimed that I had left out certain terms that usually
appear in one of the simple analytical developments I was discussing. Surprisingly, I subconscientiously immediately responded “You don’t swing at
the baseball until you get to the baseball park!” The response, of course, drew
laughter, but everyone appeared to understand the point I was trying to make.
The reason of bringing up this incident is that it is important to develop the
understanding of a phenomenon, rather than all its detailed aspects. I have
always stressed to my students that there is a great difference between knowing
something and understanding it. The relevant point is that in various sections
there have been inserted many small, important modifications to give greater
understanding to many elements of combustion that appear in the text. This
type of material did not require extensive paragraphs in each chapter section.
Most chapters in this edition contain, where appropriate, this type of important
improvement. This new material and other major additions are self-evident in
the listings in the Table of Contents.

My particular thanks go to Prof. Yetter for joining me as co-author, for
his analyzing and making small poignant modifications of the chapters that
appeared in the earlier additions, for contributing new material not covered in
these earlier additions and for further developing all the appendixes. Thanks
also go to Dr. Chris Shaddix of Sandia Livermore who made a major contribution to Chapter 9 with respect to coal combustion considerations. Our gracious
thanks go to Mary Newby of Penn State who saw to the final typing of the
complete book and who offered a great deal of general help. We would never
have made it without her. We also wish to thank our initial editor at Elsevier,
Joel Stein, for convincing us to undertake this edition of “Combustion” and
our final Editor, Matthew Hart, for seeing this endeavor through.
The last acknowledgments go to all who are recognized in the Dedication.
I initiated what I called Princeton’s Combustion Research Laboratory when I
was first appointed to the faculty there and I am pleased that Prof. Fred Dryer
now continues the philosophy of this laboratory. It is interesting to note that
Profs. Dryer and Yetter and Dr. Shaddix were always partners of this laboratory
from the time that they entered Princeton as graduate students. I thank them
again for being excellent, thoughtful, and helpful colleagues through the years.
Speaking for Prof. Yetter as well, our hope is that “Combustion, 4th
Edition” will be a worthwhile contributing and useful endeavor.
Irvin Glassman
December 2007


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Preface

When approached by the publisher Elsevier to consider writing a 4th Edition
of Combustion, we considered the challenge was to produce a book that would
extend the worthiness of the previous editions. Since the previous editions

served as a basis of understanding of the combustion field, and as a text to
be used in many class courses, we realized that, although the fundamentals
do not change, there were three factors worthy of consideration: to add and
extend all chapters so that the fundamentals could be clearly seen to provide
the background for helping solve challenging combustion problems; to enlarge
the Appendix section to provide even more convenient data tables and computational programs; and to enlarge the number of typical problem sets. More
important is the attempt to have these three factors interact so that there is a
deeper understanding of the fundamentals and applications of each chapter.
Whether this concept has been successful is up to the judgment of the reader.
Some partial examples of this approach in each chapter are given by what
follows.
Thus, Chapter 1, Chemical Thermodynamics and Flame Temperatures, is
now shown to be important in understanding scramjets. Chapter 2, Chemical
Kinetics, now explains how sensitivity analyses permit easier understanding in
the analysis of complex reaction mechanisms that endeavor to explain environmental problems. There are additions and changes in Chapter 3, Explosive and
General Oxidative Characteristics of Fuels, such as consideration of wet CO
combustion analysis, the development procedure of reaction sensitivity analysis
and the effect of supercritical conditions. Similarly the presentation in Chapter
4, Flame Phenomena in Premixed Combustible Gases, now considers flame
propagation of stratified fuel–air mixtures and flame spread over liquid fuel
spills. A point relevant to detonation engines has been inserted in Chapter 5.
Chapter 6, Diffusion Flames, more carefully analyzes the differences between
momentum and buoyant fuel jets. Ignition by pyrophoric materials, catalysts, and hypergolic fuels is now described in Chapter 7. The soot section in
Chapter 8, Environmental Combustion Considerations, has been completely
changed and also points out that most opposed jet diffusion flame experiments
must be carefully analyzed since there is a difference between the temperature
fields in opposed jet diffusion flames and simple fuel jets. Lastly, Chapter 9,
Combustion of Nonvolatile Fuels, has a completely new approach to carbon
combustion.


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Preface

The use of the new material added to the Appendices should help students
as the various new problem sets challenge them. Indeed, this approach has
changed the character of the chapters that appeared in earlier editions regardless of apparent similarity in many cases. It is the hope of the authors that the
objectives of this edition have been met.
Irvin Glassman
Richard A. Yetter


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Chapter 1

Chemical Thermodynamics and
Flame Temperatures
A. INTRODUCTION
The parameters essential for the evaluation of combustion systems are the
equilibrium product temperature and composition. If all the heat evolved in the
reaction is employed solely to raise the product temperature, this temperature
is called the adiabatic flame temperature. Because of the importance of the
temperature and gas composition in combustion considerations, it is appropriate to review those aspects of the field of chemical thermodynamics that deal
with these subjects.


B. HEATS OF REACTION AND FORMATION
All chemical reactions are accompanied by either an absorption or evolution of
energy, which usually manifests itself as heat. It is possible to determine this
amount of heat—and hence the temperature and product composition—from
very basic principles. Spectroscopic data and statistical calculations permit
one to determine the internal energy of a substance. The internal energy of a
given substance is found to be dependent upon its temperature, pressure, and
state and is independent of the means by which the state is attained. Likewise,
the change in internal energy, ΔE, of a system that results from any physical
change or chemical reaction depends only on the initial and final state of the
system. Regardless of whether the energy is evolved as heat, energy, or work,
the total change in internal energy will be the same.
If a flow reaction proceeds with negligible changes in kinetic energy and
potential energy and involves no form of work beyond that required for the
flow, the heat added is equal to the increase of enthalpy of the system
Q ϭ ΔH
where Q is the heat added and H is the enthalpy. For a nonflow reaction
proceeding at constant pressure, the heat added is also equal to the gain in
enthalpy
Q ϭ ΔH
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Combustion


and if heat evolved,
Q ϭ ϪΔH
Most thermochemical calculations are made for closed thermodynamic
systems, and the stoichiometry is most conveniently represented in terms of
the molar quantities as determined from statistical calculations. In dealing with
compressible flow problems in which it is essential to work with open thermodynamic systems, it is best to employ mass quantities. Throughout this text
uppercase symbols will be used for molar quantities and lowercase symbols
for mass quantities.
One of the most important thermodynamic facts to know about a given
chemical reaction is the change in energy or heat content associated with the
reaction at some specified temperature, where each of the reactants and products is in an appropriate standard state. This change is known either as the
energy or as the heat of reaction at the specified temperature.
The standard state means that for each state a reference state of the aggregate exists. For gases, the thermodynamic standard reference state is the ideal
gaseous state at atmospheric pressure at each temperature. The ideal gaseous
state is the case of isolated molecules, which give no interactions and obey the
equation of state of a perfect gas. The standard reference state for pure liquids
and solids at a given temperature is the real state of the substance at a pressure
of 1 atm. As discussed in Chapter 9, understanding this definition of the standard reference state is very important when considering the case of high-temperature combustion in which the product composition contains a substantial
mole fraction of a condensed phase, such as a metal oxide.
The thermodynamic symbol that represents the property of the substance in
the standard state at a given temperature is written, for example, as HTЊ , ETЊ ,
etc., where the “degree sign” superscript ° specifies the standard state, and the
subscript T the specific temperature. Statistical calculations actually permit the
determination of ET Ϫ E0, which is the energy content at a given temperature
referred to the energy content at 0 K. For 1 mol in the ideal gaseous state,
PV ϭ RT

(1.1)

H Њ ϭ E Њ ϩ ( PV )Њ ϭ E Њ ϩ RT


(1.2)

H 0Њ ϭ E0Њ

(1.3)

which at 0 K reduces to

Thus the heat content at any temperature referred to the heat or energy content
at 0 K is known and
( H Њ Ϫ H 0Њ ) ϭ ( E Њ Ϫ E0Њ ) ϩ RT ϭ ( E Њ Ϫ E0Њ ) ϩ PV

(1.4)


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3

Chemical Thermodynamics and Flame Temperatures

The value ( E Њ Ϫ E0Њ ) is determined from spectroscopic information and is
actually the energy in the internal (rotational, vibrational, and electronic)
and external (translational) degrees of freedom of the molecule. Enthalpy
( H Њ Ϫ H 0Њ ) has meaning only when there is a group of molecules, a mole for
instance; it is thus the Ability of a group of molecules with internal energy to
do PV work. In this sense, then, a single molecule can have internal energy, but
not enthalpy. As stated, the use of the lowercase symbol will signify values on a
mass basis. Since flame temperatures are calculated for a closed thermodynamic

system and molar conservation is not required, working on a molar basis is most
convenient. In flame propagation or reacting flows through nozzles, conservation of mass is a requirement for a convenient solution; thus when these systems
are considered, the per unit mass basis of the thermochemical properties is used.
From the definition of the heat of reaction, Qp will depend on the temperature T at which the reaction and product enthalpies are evaluated. The heat of
reaction at one temperature T0 can be related to that at another temperature T1.
Consider the reaction configuration shown in Fig. 1.1. According to the First
Law of Thermodynamics, the heat changes that proceed from reactants at temperature T0 to products at temperature T1, by either path A or path B must be
the same. Path A raises the reactants from temperature T0 to T1, and reacts
at T1. Path B reacts at T0 and raises the products from T0 to T1. This energy
equality, which relates the heats of reaction at the two different temperatures,
is written as
⎧⎪
⎡
⎪
⎨ ∑ n j ⎢ HTЊ1 Ϫ H 0Њ Ϫ HTЊ0 Ϫ H 0Њ
⎪⎪ j ,react ⎣
⎪⎩
⎧
⎡
ϭ ΔHT0 ϩ ⎪⎪⎨ ∑ ni ⎢ HTЊ1 Ϫ H 0Њ
⎪⎪⎩ i,prod ⎣

) (

(

(

⎫⎪


)⎤⎥⎦ ⎪⎬⎪⎪ ϩ ΔHH
j

⎪⎭

) Ϫ ( HЊ

T0

T1

⎤ ⎫
Ϫ H 0Њ ⎥ ⎪⎪⎬
⎦i ⎪
⎪⎭

)

(1.5)

where n specifies the number of moles of the ith product or jth reactant. Any
phase changes can be included in the heat content terms. Thus, by knowing the
difference in energy content at the different temperatures for the products and

(1Ј)

ΔHT1

(2Ј)


T1

Path A

(1)

Path B

(2)

T0

ΔHT0
Reactants

Products

FIGURE 1.1 Heats of reactions at different base temperatures.